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arXiv:2511.12475

Vortex states and entanglement properties in multiphoton pair production

Hong-Hao Fan, Lie-Juan Li, Zhi-Hang Yao, Orkash Amat, Suo Tang, Bai-Song Xie

hep-phquant-phSubmitted Nov 16, 2025• Announced Nov 18, 2025
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Abstract

We investigate the multiphoton pair production in circularly polarized field via two level model. There appears obvious discrete ring structures in the momentum distribution of the created particles, in which the ring radius is mainly controlled by the number of the photons absorbed in the creation with the energy conservation and could also be modulated by the spin of the created pair. These multiphoton rings become narrower when both of the pair particles' spin are aligned with the direction of the field rotation, and become broader if both spin are antiparallel to that direction. This spin-modulation can be simply understood with the angular momentum conservation, as less orbital angular momentum from the absorbed photons would be transferred to the created particles if their spins are aligned with the field rotation. The orbital angular momentum of the created particles is manifested as the vortex structure in the phase of the momentum distribution, and valued as the topological charge of this phase vortex. We also study the spin entanglement between the created particles, and reveal that the entanglement becomes stronger with the increase of the particles' transverse momentum, and gets sharp peak in the transition between different multiphoton rings, where the topological charge of the phase vortex is changed.

Comments
22 pages, 5 figures

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We investigate the multiphoton pair production in circularly polarized field via two level model. There appears obvious discrete ring structures in the momentum distribution of the created particles, in which the ring radius is mainly controlled by the number of the photons absorbed in the creation with the energy conservation and could also be modulated by the spin of the created pair. These multiphoton rings become narrower when both of the pair particles' spin are aligned with the direction of the field rotation, and become broader if both spin are antiparallel to that direction. This spin-modulation can be simply understood with the angular momentum conservation, as less orbital angular momentum from the absorbed photons would be transferred to the created particles if their spins are aligned with the field rotation. The orbital angular momentum of the created particles is manifested as the vortex structure in the phase of the momentum distribution, and valued as the topological charge of this phase vortex. We also study the spin entanglement between the created particles, and reveal that the entanglement becomes stronger with the increase of the particles' transverse momentum, and gets sharp peak in the transition between different multiphoton rings, where the topological charge of the phase vortex is changed.
The vortex structures in the momentum distributions of multiple particle-antiparticle pairs produced from the vacuum by a spatially uniform, time-varying electric field with arbitrary polarization are investigated using the Bogoliubov transformation. For linearly polarized fields, as the field strength increases, the nodal lines in the multi-pair momentum distribution break up into vortex-antivortex pairs in both the bosonic and fermionic cases. Each vortex carries a topological charge that is an integer multiple of the single-pair vortex topological charge. For circular polarization, a central vortex appears at all field strengths. For bosons, its topological charge is an integer multiple of the single-pair vortex topological charge; for fermions, it is an integer multiple of the vortex topological charge for single-pair production with zero total spin projection along the field propagation direction. For elliptical polarization with suitable ellipticity, discrete vortices coexist with a central vortex. In this case, however, the integer-multiple relation for fermions generally fails because the two-pair production amplitude is a determinant and spin-channel contributions are separated in momentum space. These results provide a theoretical basis for understanding the vortex topology of multi-pair production in strong-field QED and for its potential control.
We investigate spin-resolved momentum distributions and phase vortices in multiphoton electron-positron pair production within a modified two-level model. This model retains the diagonal spinor inner-product terms neglected in the adiabatic approximation, thereby inducing spin-resolved transverse asymmetries in the momentum distribution. For a circularly polarized pulse, the handedness determines the winding direction of the quantized vortices, whereas for a linearly polarized pulse, the phase distribution exhibits nodal lines rather than quantized vortices. For two time-delayed circularly polarized pulses, the time delay introduces a relative phase that governs the multiphoton interference, which in turn drives the vortex evolution in each spin configuration. These results demonstrate that pulse polarization and time delay enable coherent control over vortex topology in pair production.
Photons carry one unit of angular momentum associated with their spin~\cite{Beth1936}. Structured vortex beams carry additional orbital angular momentum which can also be transferred to matter~\cite{Allen1992}. This extra twist has been used for example to drive motion of microscopic particles in optical tweezers as well as to create vortices in degenerate quantum gases~\cite{He1995,Andersen2006}. Here we demonstrate the transfer of optical orbital angular momentum from the transverse spatial structure of the beam to the internal (electronic) degrees of freedom of an atom. Probing a quadrupole transition of a single trapped 40^{40}40Ca+^++ ion localized at the center of the vortex, we observe strongly modified selection rules, accounting for both the photon spin and the vorticity of the field. In particular, we show that an atom can absorb two quanta of angular momentum from a single photon even when rotational symmetry is conserved. In contrast to previous findings~\cite{Araoka2005,Loeffler2011a,Mathevet2013}, our experiment allows for conditions where the vorticity of the laser beam determines the optical excitation, contributing to the long-standing discussion on whether the orbital angular momentum of photons can be transferred to atomic internal degrees of freedom~\cite{VanEnk1994,Babiker2002,Jauregui2004, Schmiegelow2012, Mondal2014, Scholz-Marggraf2014} and paves the way for its use to tailor light-matter interactions.
We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of variant Planck's over 2pi, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.
It is shown that the spin and orbital angular momentum of electric dipole photons have the same operator structure and may differ from each other only by spatial dependence in the very vicinity of the atom. It is shown that the photon twins created by a dipole forbidden transition can manifest the maximum entanglement with respect to the angular momentum. It is shown that the states of photons with projection of angular momentum m=0m=0m=0 are less stable than those with m=±1m= \pm 1m=±1.
Abstract Up-conversion in an atomic vapor is known to produce photon pairs. If addressed by vortex beams, it produces pairs of orbital angular momenta (OAM), that are valuable bricks for quantum processes with OAM. The perfect vortex (PV) beam is a vortex class very pertinent in this context, because its ring radius and its Gouy phase are —in principle— independent of the OAM, giving a huge spiral bandwidth compared to the usual Laguerre-Gaussian (LG) beam. Our experimental study clarifies this point. The PV ring radius and thickness are found to vary hyperbolic-like vs . the OAM, which will limit the spiral bandwidth, but, unlike LG, the number of generated OAM pairs still remains quite comfortable for entanglement applications.